We present an updated catalog of X-ray point sources in the inner 500" (~20pc) of the Galactic center (GC), where the nuclear star cluster (NSC) stands, based on a total of ~4.5Ms of Chandra observations taken from 1999 September to 2013 April. This ultradeep data set offers unprecedented sensitivity for detecting X-ray sources in the GC, down to an intrinsic 2-10keV luminosity of 1.0x10^31^erg/s. A total of 3619 sources are detected in the 2-8keV band, among which ~3500 are probable GC sources and ~1300 are new identifications. The GC sources collectively account for ~20% of the total 2-8keV flux from the inner 250" region where detection sensitivity is the greatest. Taking advantage of this unprecedented sample of faint X-ray sources that primarily traces the old stellar populations in the NSC, we revisit global source properties, including long-term variability, cumulative spectra, luminosity function, and spatial distribution. Based on the equivalent width and relative strength of the iron lines, we suggest that in addition to the arguably predominant population of magnetic cataclysmic variables (CVs), nonmagnetic CVs contribute substantially to the detected sources, especially in the lower-luminosity group. On the other hand, the X-ray sources have a radial distribution closely following the stellar mass distribution in the NSC, but much flatter than that of the known X-ray transients, which are presumably low-mass X-ray binaries (LMXBs) caught in outburst. This, together with the very modest long-term variability of the detected sources, strongly suggests that quiescent LMXBs are a minor (less than a few percent) population.